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On the smoothness of convex envelopes


Authors: A. Griewank and P. J. Rabier
Journal: Trans. Amer. Math. Soc. 322 (1990), 691-709
MSC: Primary 49J52; Secondary 90C30
DOI: https://doi.org/10.1090/S0002-9947-1990-0986024-2
MathSciNet review: 986024
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Abstract: We examine differentiability properties of the convex envelope $ \operatorname{conv} E$ of a given function $ E:{{\mathbf{R}}^n} \to ( - \infty ,\infty ]$ in terms of properties of $ E$. It is shown that $ {C^1}$ as well as optimal $ {C^{1,\alpha }}$ regularity results, $ 0 < \alpha \leqslant 1$, can be obtained under general conditions.

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DOI: https://doi.org/10.1090/S0002-9947-1990-0986024-2
Article copyright: © Copyright 1990 American Mathematical Society

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